1. Calculation Session 1 Lecture 2:
Rate equations from experimental data; concentration vs. time
method of initial rates
isolation method
integrated rate equations
method of half lives
Defining Question:
How to best assess graphically an empirical fit to experimental data?
Discussion
Quizzes or No Quizzes?
Exercises 1, 2, 4, and 3.
Work in groups
Solutions will be presented in class
Solutions will be posted:

2. Rate Equations from Experimental Data
A  P
irreversible
rate equation?
assume
a = ?
usually a = 0, 1/2, 1, 3/2, or 2

3. Rate Equations from Experimental Data
0.06
0.05
0.04
[A] (mol/L) .
0.03
0.02
0.01
100
200
300
400
500
600
700
800
time (sec)

4. half order: rate = k[A]1/2
Reaction Order?
How to Find
Guess “a” and fit a line to the data?
2nd order: rate = k[A]2
half order: rate = k[A]1/2
1st order: rate = k[A]
zero order: rate = k

5. Reaction Order? Better to plot the data as a straight line.
equation for a
straight line on
a log-log plot x y
slope
intercept

6. How to convert concentration vs. time to rate vs. concentration?
Measure slopes!
0.06
(0, 0.044)
0.05
0.0440
0.04
[A] (mol/L) .
0.03
0.0252
0.02
0.0110
0.01
100
200
300
400
500
600
700
800
time (sec)
(500, 0)

7. Method of Initial Rates
0.001
(0.3, 0.001)
Reasonable? dt
[A]/
0.0001 d -
(0.01, )
0.01
0.1 1
[A]

8. Isolation Method More than one reactant? Isolate the effects of [A].
A + B  P
B is in excess.
[B]  [B]0
[B] is ~constant

9. Integrated Rate Equations: First-Order Reactions1
important:
add integration limits
separate …
and integrate.
equation for a straight line

10. Integrated Rate Equations: First-Order Reactions, A  P
(0, 1)
straight line
confirms
1st-order
reaction
(800, 0.052)

11. Integrated Rate Equations: Second-Order Reactions
separate and integrate.
equation for a straight line

12. Integrated Rate Equations: Second-Order Reactions, 2A  P
Example: Dimerization of Butadiene
2C4H6  C8H12
slope = k = 0.86 L/(mol·min)
straight line
confirms
2nd-order
reaction

13. Integrated Rate Equations: Half Lives
t½  the time for a reactant concentration to decrease to ½ its initial value
First Order Reaction:
substitute [A] = ½[A]0
at t = t½
If t½ is independent of [A],
reaction is first order and irreversible.

14. Integrated Rate Equations: Half Lives
t½  the time for a reactant concentration to decrease to ½ its initial value
Second Order Reaction:
substitute [A] = ½[A]0
at t = t½
Plot t½ vs. 1/[A]0. If line is straight,
reaction is second order and irreversible.

15. Integrated Rate Equations: Half Lives
nth Order Reaction:
need an integrated equation.
substitute [A] = ½[A]0 at t = t½
okay for n = 1?
L’Hôpital!
straight line! y x
slope
intercept

16. Integrated Rate Equations: Half Lives
Dimerization of Butadiene: 2C4H6  C8H12 18 17 1 16 2 14 3 12 11
mol/L 4 3 10
] x 10 5 8 H 6 4 [C 6 4 2 20 40 60 80
100
120
140
160
180
200
35 min
time (min)

17. Integrated Rate Equations: Half Lives
Dimerization of Butadiene: 2C4H6  C8H12
(0.0012, 1000)
slope = -1/2
(0.1, 12)
reasonable?
slope = -2

18. 7 Logarithmic Scales log102 = 0.30 log1020 = 1.30 log10x x: x 10x:4 5 6 8 9 20 30 40 60 80
100 = 1
100.4 = 2.51
101 = 10
101.4 = 25.1
102 = 100

19. Logarithmic Scales log(ab) = log(a) + log(b) +0.6 1.2 + 0.6 = 1.8 5
8  5 = 40 3
4  3 = 12
How to plot 12? 3
50  3 = 16.7
How to plot 17?

20. Logarithmic Scales Another method to plot numbers.
distance from 1 to 10 = 105 mm
distance from 1 to 17 = x mm
129 mm
A method to read numbers.
77 mm
distance from 1 to 10 = 105 mm
distance from 1 to x = 77 mm